Abstract
A heuristic algorithm is designed to searching for good higher dimensional self-orthogonal codes over GF(A) from low dimensional self-orthogonal codes. Many self-orthogonal codes of length 20 les n les 36 and dual distance 5 or 6 are obtained, and several have improved dual distance. Consequently, using these self-orthogonal codes and their dual codes, some linear quantum codes of minimum distance five or six for such length n are obtained, and three of these codes [[24, 8, 5]], [[25, 9, 5]], [[27, 7, 6]] are record-breaking. Quaternary code, self-orthogonal code, linear quantum error-correcting code.
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